Remark 1 From Corollary REF  we obtain that \( \sigma _{M_{n}} \)  are bounded from \( H_p \)  to \( H_p \) , but from Corollary REF  we conclude that \( \sigma _{M_{n}+1} \)  are not bounded from \( H_p \)  to \( H_p \) . The main reason is that Fourier coefficients of martingales \( f\in H_p \)  are not uniformly bounded (for details see e.g. [1]}).

